Use the Formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$

question 36

Multiple Choice

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b )$ $C = \arctan ( a / b ) , a > 0$ ,to rewrite the trigonometric expression in the form $a \sin B \theta + b \cos B \theta$ ​ 9 $\cos \left( \theta - \frac { \pi } { 4 } \right)$ ​

• A) \(\frac { 9 \sqrt { 2 } } { 2 } \cos \theta\)
• B) \[- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta\]
• C) \[- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta\]
• D) \(\frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta\)
• E) \(\frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta\)

---

Definitions:

Contingent Avoidance

A type of learning where a subject learns to perform a behavior to prevent the occurrence of an aversive stimulus.

Active Avoidance

A learning process in which an organism learns to perform a behavior to prevent or avoid an unpleasant stimulus.

Negative Reinforcement

The strengthening of a behavior by removing or avoiding a negative outcome or aversive stimulus when the behavior is performed.

Escape Response

A behavior aimed at moving away from or avoiding an unpleasant stimulus or situation, often studied in the context of aversive conditioning.